Theorem 3an6 1333

Description: Analog of an4 586 for triple conjunction. (Contributed by Scott Fenton, 16-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.)

Assertion

Ref	Expression
3an6	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) /\ ( ta /\ et ) ) <-> ( ( ph /\ ch /\ ta ) /\ ( ps /\ th /\ et ) ) )

Proof of Theorem 3an6

Step	Hyp	Ref	Expression
1		an6 1332	. 2 |- ( ( ( ph /\ ch /\ ta ) /\ ( ps /\ th /\ et ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) /\ ( ta /\ et ) ) )
2	1	bicomi 132	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) /\ ( ta /\ et ) ) <-> ( ( ph /\ ch /\ ta ) /\ ( ps /\ th /\ et ) ) )

Syntax hints:   /\ wa 104   <-> wb 105   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  poxp  6290